Variations of Box PlotsAbstract Box plots display batches of data. Five values from a set of data are conventionally used; the extremes, the upper and lower hinges (quartiles), and the median. Such plots are becoming a widely used tool in exploratory data analysis and in preparing visual summaries for statisticians and nonstatisticians alike. Three variants of the basic display, devised by the authors, are described. The first visually incorporates a measure of group size; the second incorporates an indication of rough significance of differences between medians; the third combines the features of the first two. These techniques are displayed by examples.
Variations of Box PlotsThe Use of Partial Residual Plots in Regression AnalysisThis paper defines partial residuals in multiple linear regression. The ith partial residual vector can be thought of as the dependent variable vector corrected for all independent variables except the ith variable. A plot of the ith partial residuals vs values of the ith variable is proposed as a replacement for the usual plot displaying ordinary residuals vs the ith independent variable. This partial residual plot shows the extent and direction of linearity, while displaying deviations from linearity, such as outliers, inhomogeneity of variance, and curvilinear relationships. Some alternative definitions of partial residuals are described.
Performance testing of color‐difference metrics using a color tolerance datasetDavid H. Alman, Roy S. Berns, Gregory D. Snyder et al.|Color Research & Application|1989 Abstract A color‐difference dataset was developed for testing the performance of color metrics. The dataset comprises 45 color‐difference vectors varying in five directions at nine color centers under conditions typical of commercial color decisions. Probit analysis was used to estimate the parameters of the population distribution of tolerances for each vector. In addition to estimating the median tolerance, the anlysis allows one to estimate the uncertainty of a tolerance and to test the adequacy of the underlying model tolerance distribution. The median tolerances were used to specify 45 color‐difference pairs with equal visual color‐difference magnitudes. The performance of eight color‐difference metrics was compared using the normalized standard deviation of the color differences of the visually equal difference pairs as a measure of uniformity. A bootstrap statistical technique was used to quantify the variation in performance with varying samples of color centers and color‐difference directions and to determine the significance of observed differences in uniformity performance. Some metrics based on weighted CIELAB dl*, dC*, dH* color‐difference components had significantly superior performance compared to the CIE recommended color‐difference metrics.
The Use of Partial Residual Plots in Regression AnalysisThis paper defines partial residuals in multiple linear regression. The ith partial residual vector can be thought of as the dependent variable vector corrected for all independent variables except the ith variable. A plot of the ith partial residuals vs values of the ith variable is proposed as a replacement for the usual plot displaying ordinary residuals vs the ith independent variable. This partial residual plot shows the extent and direction of linearity, while displaying deviations from linearity, such as outliers, inhomogeneity of variance, and curvilinear relationships. Some alternative definitions of partial residuals are described.